A172237 - OEIS

A172237

T(n,k) = T(n-1,k) + k*T(n-2,k) for k >= 1 and n >= 3 with T(0,k) = 0 and T(1,k) = T(2,k) = 1 for all k >= 1; array T(n,k), read by descending antidiagonals, with n >= 0 and k >= 1.

0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 3, 3, 0, 1, 1, 4, 5, 5, 0, 1, 1, 5, 7, 11, 8, 0, 1, 1, 6, 9, 19, 21, 13, 0, 1, 1, 7, 11, 29, 40, 43, 21, 0, 1, 1, 8, 13, 41, 65, 97, 85, 34, 0, 1, 1, 9, 15, 55, 96, 181, 217, 171, 55, 0, 1, 1, 10, 17, 71, 133, 301, 441, 508, 341, 89, 0, 1, 1, 11

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OFFSET

0,10

COMMENTS

Transposed variant of A083856, without the top row of A083856.

Antidiagonal sums are (0, 1, 2, 4, 8, 16, 33, 70, 153, 345, ...) = (A110113(n) - 1: n >= 1).

Characteristic polynomials for columns are y^2 - y - k.

LINKS

Table of n, a(n) for n=0..81.

EXAMPLE

Array T(n,k) (with rows n >= 0 and columns k >= 1) begins as follows:

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ...

5, 11, 19, 29, 41, 55, 71, 89, 109, 131, ...

8, 21, 40, 65, 96, 133, 176, 225, 280, 341, ...

13, 43, 97, 181, 301, 463, 673, 937, 1261, 1651, ...

21, 85, 217, 441, 781, 1261, 1905, 2737, 3781, 5061, ...

34, 171, 508, 1165, 2286, 4039, 6616, 10233, 15130, 21571, ...

55, 341, 1159, 2929, 6191, 11605, 19951, 32129, 49159, 72181, ...

...

MAPLE

A172237 := proc(n, k)

if n = 0 then

elif n <=2 then

1 ;

else

procname(n-1, k)+k*procname(n-2, k) ;

end if;

end proc: # R. J. Mathar, Jul 05 2012

MATHEMATICA

f[0, a_] := 0; f[1, a_] := 1;

f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];

m1 = Table[f[n, a], {n, 0, 10}, {a, 1, 11}];

Table[Table[m1[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Cf. A083856, A110113, A193376.

Sequence in context: A035788 A097559 A293108 * A246181 A123226 A347382

Adjacent sequences: A172234 A172235 A172236 * A172238 A172239 A172240

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jan 29 2010

EXTENSIONS

More terms from Petros Hadjicostas, Dec 26 2019

STATUS

approved