A329755 Doubly hexagonal pyramidal numbers.

0, 1, 252, 7337, 84575, 576080, 2795121, 10700382, 34388362, 96606475, 243939410, 564840991, 1217275137, 2469392562, 4757404575, 8765621740, 15534503236, 26603512517, 44196596312, 71459197125, 112756874195, 174046844356, 263335062397, 391232840362, 571628456750, 822490729775

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Hexagonal 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 + 242*x + 4862*x^2 + 22425*x^3 + 30465*x^4 + 12424*x^5 + 1248*x^6 + 13*x^7)/(1 - x)^10.

a(n) = A002412(A002412(n)).

a(n) = Sum_{k=0..A002412(n)} A000384(k).

a(n) = n *(4*n-1) *(n+1) *(4*n^3+3*n^2-n+6) *(8*n^3+6*n^2-2*n-3) / 648 . - R. J. Mathar, Nov 28 2019

Mathematica

A002412[n_] := n (n + 1) (4 n - 1)/6; a[n_] := A002412[A002412[n]]; Table[a[n], {n, 0, 25}]
Table[Sum[k (2 k - 1), {k, 0, n (n + 1) (4 n - 1)/6}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[x (1 + 242 x + 4862 x^2 + 22425 x^3 + 30465 x^4 + 12424 x^5 + 1248 x^6 + 13 x^7)/(1 - x)^10, {x, 0, nmax}], x]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 252, 7337, 84575, 576080, 2795121, 10700382, 34388362, 96606475}, 26]

Crossrefs

Cf. A000384, A002412, A063249, A140236, A329753, A329754, A329756, A329757.

Sequence in context: A270853 A177301 A250376 * A109924 A281032 A047831

Adjacent sequences: A329752 A329753 A329754 * A329756 A329757 A329758

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 20 2019

Status

approved