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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
OFFSET
1,1
COMMENTS
Sequence extended to n=1 using recurrence. - Andrew Howroyd, Jun 19 2017
LINKS
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
Sequence in context: A026024 A026542 A028045 * A024438 A025999 A028058
KEYWORD
nonn,changed
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