editing

approved

A026820 := proc(n, k) if k > n then combinat[numbpart](n, n) ; else combinat[numbpart](n, k) ; fi ; end: A115994 := proc(n, k) local i ; add(A026820(i, k)*A026820(n-k^2-i, k), i=0..n-k^2) ; end: A117488 := proc(n, k) if k >= 2*n then 0 ; else if n = 1 then 1; else A115994(k+n^2-2*n, n-1) ; fi ; fi ; end: for n from 1 to 10 do for k from 1 to 2*n-1 do printf("%d ", A117488(n, k)) ; od ; od ; - _# _R. J. Mathar_, Feb 22 2007

approved

editing

_Alford Arnold (Alford1940(AT)aol.com), _, Mar 22 2006

A026820 := proc(n, k) if k > n then combinat[numbpart](n, n) ; else combinat[numbpart](n, k) ; fi ; end: A115994 := proc(n, k) local i ; add(A026820(i, k)*A026820(n-k^2-i, k), i=0..n-k^2) ; end: A117488 := proc(n, k) if k >= 2*n then 0 ; else if n = 1 then 1; else A115994(k+n^2-2*n, n-1) ; fi ; fi ; end: for n from 1 to 10 do for k from 1 to 2*n-1 do printf("%d ", A117488(n, k)) ; od ; od ; - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Feb 22 2007

More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Feb 22 2007

A026820 := proc(n, k) if k > n then combinat[numbpart](n, n) ; else combinat[numbpart](n, k) ; fi ; end: A115994 := proc(n, k) local i ; add(A026820(i, k)*A026820(n-k^2-i, k), i=0..n-k^2) ; end: A117488 := proc(n, k) if k >= 2*n then 0 ; else if n = 1 then 1; else A115994(k+n^2-2*n, n-1) ; fi ; fi ; end: for n from 1 to 10 do for k from 1 to 2*n-1 do printf("%d ", A117488(n, k)) ; od ; od ; - Richard R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2007

tabf,nonn,new

More terms from Richard R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2007

The number one 1 followed by 2*k+1 terms from column k of table A115994.

1, 1, 2, 3, 1, 2, 5, 8, 14, 1, 2, 5, 10, 18, 30, 49, 1, 2, 5, 10, 20, 34, 59, 94, 149, 1, 2, 5, 10, 20, 36, 63, 104, 169, 264, 405, 1, 2, 5, 10, 20, 36, 65, 108, 179, 284, 445, 676, 1017, 1, 2, 5, 10, 20, 36, 65, 110, 183, 294, 465, 716, 1089, 1622, 2387, 1, 2, 5, 10, 20, 36, 65

Triangle starts

1

1 2 3

1 2 5 8 14

1 2 5 10 18 30 49

1 2 5 10 20 34 59 94 149

1 2 5 10 20 36 63 104 169 264 405

1 2 5 10 20 36 65 108 179 284 445 676 1017

1 2 5 10 20 36 65 110 183 294 465 716 1089 1622 2387

A026820 := proc(n, k) if k > n then combinat[numbpart](n, n) ; else combinat[numbpart](n, k) ; fi ; end: A115994 := proc(n, k) local i ; add(A026820(i, k)*A026820(n-k^2-i, k), i=0..n-k^2) ; end: A117488 := proc(n, k) if k >= 2*n then 0 ; else if n = 1 then 1; else A115994(k+n^2-2*n, n-1) ; fi ; fi ; end: for n from 1 to 10 do for k from 1 to 2*n-1 do printf("%d ", A117488(n, k)) ; od ; od ; - Richard J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2007

more,tabf,nonn,new

More terms from Richard J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2007

The number one followed by 2*k+1 terms from column k of table A115994.

1, 1, 2, 3, 1, 2, 5, 8, 14, 1, 2, 5, 10, 18, 30, 49, 1, 2, 5, 10, 20, 34, 59, 94, 149

1,3

Column two of table A115994 begins 1 2 5 8 14 20 30 ... A006918

so row three of A117488 is 1 2 5 8 14.

Cf. A006918, A115994, A117489.

more,nonn

Alford Arnold (Alford1940(AT)aol.com), Mar 22 2006

approved