OFFSET
0,2
COMMENTS
Similar sequences of the type m*P(s,m) - Sum_{i=1..m} P(s-1,i), where P(s,m) is the m-th s-gonal number:
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Wikipedia, Polygonal numbers: Table of values.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: x*(7 + 4*x)/(1 - x)^4.
a(-n) = -A132112(n-1).
a(n) = Sum_{k=0..n} A011875(11*k+2).
Equivalently, partial sums of A254963.
E.g.f.: x*(42 + 54*x + 11*x^2)*exp(x)/6. - G. C. Greubel, Mar 31 2021
EXAMPLE
MAPLE
MATHEMATICA
Table[n (n + 1) (11 n + 10)/6, {n, 0, 40}]
Column[CoefficientList[Series[x (7 + 4 x) / (1 - x)^4, {x, 0, 60}], x]] (* Vincenzo Librandi, Jan 31 2015 *)
PROG
(PARI) vector(40, n, n--; n*(n+1)*(11*n+10)/6)
(Sage) [n*(n+1)*(11*n+10)/6 for n in (0..40)]
(Magma) [n*(n+1)*(11*n+10)/6: n in [0..40]];
(Maxima) makelist(n*(n+1)*(11*n+10)/6, n, 0, 40);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jan 30 2015
STATUS
approved