A288714 Number of (undirected) paths on the 2n-crossed prism graph.

26, 444, 3654, 22888, 124850, 628860, 3014438, 13987152, 63462906, 283337380, 1249770830, 5460869112, 23680912034, 102049764684, 437447065590, 1866647382688, 7933717075274, 33602668068852, 141880252869278, 597395676419400, 2509073159290866, 10514236156062364

Offset

1,1

Comments

Sequence extended to n=1 using recurrence. - Andrew Howroyd, Jun 19 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Eric Weisstein's World of Mathematics, Graph Path

Index entries for linear recurrences with constant coefficients, signature (16, -105, 366, -732, 840, -512, 128).

Formula

a(n) = n*(163*4^n-9*2^(n+3)*n-87*2^(n+1)-4)/6.

From Andrew Howroyd, Jun 19 2017: (Start)

a(n) = 16*a(n-1)-105*a(n-2)+366*a(n-3)-732*a(n-4) +840*a(n-5)-512*a(n-6)+128*a(n-7) for n>7.

G.f.: 2*x*(13+14*x-360*x^2+764*x^3-580*x^4+152*x^5)/((1-x)^2*(1-2*x)^3*(1-4*x)^2).

(End)

Mathematica

Table[n (163 4^n - 9 2^(n + 3) n - 87 2^(n + 1) - 4)/6, {n, 20}]
LinearRecurrence[{16, -105, 366, -732, 840, -512, 128}, {26, 444, 3654, 22888, 124850, 628860, 3014438}, 20]
CoefficientList[Series[-((2 (13 + 14 x - 360 x^2 + 764 x^3 - 580 x^4 + 152 x^5))/((-1 + 2 x)^3 (1 - 5 x + 4 x^2)^2)), {x, 0, 20}], x]

Prog

(PARI)
Vec(2*(13+14*x-360*x^2+764*x^3-580*x^4+152*x^5)/((1-x)^2*(1-2*x)^3*(1-4*x)^2) + O(x^20)) \\ Andrew Howroyd, Jun 19 2017

Crossrefs

Cf. A234617, A137885.

Sequence in context: A026024 A026542 A028045 * A024438 A025999 A028058

Adjacent sequences: A288711 A288712 A288713 * A288715 A288716 A288717

Keyword

nonn

Author

Eric W. Weisstein, Jun 13 2017

Extensions

a(1) prepended and terms a(11) and beyond from Andrew Howroyd, Jun 19 2017

Status

approved