A307918 Number of (undirected) paths in the n-dipyramidal graph.

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

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