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A307918 Number of (undirected) paths in the n-dipyramidal graph. 0
3, 26, 111, 396, 1235, 3414, 8463, 19064, 39555, 76530, 139535, 241860, 401427, 641774, 993135, 1493616, 2190467, 3141450, 4416303, 6098300, 8285907, 11094534, 14658383, 19132392, 24694275, 31546658, 39919311, 50071476, 62294291, 76913310, 94291119, 114830048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Extended to a(1)-a(2) using the formula/recurrence.

LINKS

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Graph Path

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n) = n*(-135 + 293*n - 180*n^2 + 80*n^3 - 15*n^4 + 2*n^5)/15.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: x*(-3 - 5*x + 8*x^2 - 60*x^3 + 11*x^4 - 47*x^5)/(-1 + x)^7.

MATHEMATICA

Table[n (-135 + 293 n - 180 n^2 + 80 n^3 - 15 n^4 + 2 n^5)/15, {n, 20}]

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {3, 26, 111, 396, 1235, 3414, 8463}, 20]

CoefficientList[Series[(-3 - 5 x + 8 x^2 - 60 x^3 + 11 x^4 - 47 x^5)/(-1 + x)^7, {x, 0, 20}], x]

CROSSREFS

Sequence in context: A169832 A322300 A100606 * A055330 A034495 A034493

Adjacent sequences:  A307915 A307916 A307917 * A307919 A307920 A307921

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, May 06 2019

STATUS

approved

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Last modified June 15 19:31 EDT 2021. Contains 345049 sequences. (Running on oeis4.)