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A288714 Number of (undirected) paths on the 2n-crossed prism graph. 1
26, 444, 3654, 22888, 124850, 628860, 3014438, 13987152, 63462906, 283337380, 1249770830, 5460869112, 23680912034, 102049764684, 437447065590, 1866647382688, 7933717075274, 33602668068852, 141880252869278, 597395676419400, 2509073159290866, 10514236156062364 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 22:15 EST 2020. Contains 332312 sequences. (Running on oeis4.)