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
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