A329756 Doubly heptagonal pyramidal numbers.

0, 1, 456, 14976, 181780, 1273970, 6293756, 24395756, 79119496, 223821235, 568280240, 1321714636, 2858876956, 5817509516, 11237224740, 20751835560, 36849296016, 63215722181, 105182448536, 170297734920, 269047574180, 415753060646, 629674964556, 936359517556

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Heptagonal Pyramidal Number

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: x*(1 + 446*x + 10461*x^2 + 52420*x^3 + 75580*x^4 + 32544*x^5 + 3504*x^6 + 44*x^7)/(1 - x)^10.

a(n) = A002413(A002413(n)).

a(n) = Sum_{k=0..A002413(n)} A000566(k).

a(n) = n *(5*n-2) *(n+1) *(5*n^3+3*n^2-2*n+6) *(25*n^3+15*n^2-10*n-12)/1296. - R. J. Mathar, Nov 28 2019

Mathematica

A002413[n_] := n (n + 1) (5 n - 2)/6; a[n_] := A002413[A002413[n]]; Table[a[n], {n, 0, 25}]
Table[Sum[k (5 k - 3)/2, {k, 0, n (n + 1) (5 n - 2)/6}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[x (1 + 446 x + 10461 x^2 + 52420 x^3 + 75580 x^4 + 32544 x^5 + 3504 x^6 + 44 x^7)/(1 - x)^10, {x, 0, nmax}], x]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 456, 14976, 181780, 1273970, 6293756, 24395756, 79119496, 223821235}, 26]

Crossrefs

Cf. A000566, A002413, A140236, A264891, A329753, A329754, A329755, A329757.

Sequence in context: A222552 A200784 A077578 * A268162 A223750 A048110

Adjacent sequences: A329753 A329754 A329755 * A329757 A329758 A329759

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 20 2019

Status

approved