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A329755 Doubly hexagonal pyramidal numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 13 21:24 EDT 2021. Contains 342941 sequences. (Running on oeis4.)