OFFSET
0,3
COMMENTS
Similar sequences, where P(s, m) = ((s-2)*m^2-(s-4)*m)/2 is the m-th s-gonal number:
A000578: P(3, m)*P( 3, m) - P(3, m-1)*P( 3, m-1);
A213772: P(3, m)*P( 4, m) - P(3, m-1)*P( 4, m-1) for m>0;
A005915: P(3, m)*P( 5, m) - P(3, m-1)*P( 5, m-1) " ;
A130748: P(3, m)*P( 6, m) - P(3, m-1)*P( 6, m-1) for m>1;
A027849: P(3, m)*P( 7, m) - P(3, m-1)*P( 7, m-1) for m>0;
A214092: P(3, m)*P( 8, m) - P(3, m-1)*P( 8, m-1) " ;
A100162: P(3, m)*P( 9, m) - P(3, m-1)*P( 9, m-1) " ;
A260260: P(3, m)*P(10, m) - P(3, m-1)*P(10, m-1), this sequence;
A100165: P(3, m)*P(11, m) - P(3, m-1)*P(11, m-1) for m>0.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
OEIS Wiki, Figurate numbers.
Wikipedia, Polygonal numbers: Table of values.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: x*(1 + 25*x + 22*x^2)/(1 - x)^4. [corrected by Georg Fischer, May 10 2019]
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 4. - Wesley Ivan Hurt, Dec 18 2020
MATHEMATICA
Table[n (16 n^2 - 21 n + 7)/2, {n, 0, 40}]
PROG
(PARI) vector(40, n, n--; n*(16*n^2-21*n+7)/2)
(Sage) [n*(16*n^2-21*n+7)/2 for n in (0..40)]
(Magma) [n*(16*n^2-21*n+7)/2: n in [0..40]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jul 21 2015
STATUS
approved