OFFSET
1,1
COMMENTS
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
FORMULA
O.g.f.: 64*x*(64 + 665*x + 116536*x^2 + 140505*x^3 + 2023280*x^4 + 983830*x^5 + 4720240*x^6 + 983830*x^7 + 2023280*x^8 + 140505*x^9 + 116536*x^10 + 665*x^11 + 64*x^12)/((1 + x)^6*(1 - x)^7).
E.g.f.: (-8192 + 45*(91 + 182*x - 5250*x^2 + 16000*x^3 - 9375*x^4 + 1250*x^5)*exp(-x) + (4097 + 287000*x^2 + 1262500*x^3 + 1253125*x^4 + 375000*x^5 + 31250*x^6)*exp(x))/2.
a(n) = (10*n - 3*(-1)^n - 5)^6/64 = 64*A047221(n)^6.
MATHEMATICA
Table[(10 n - 3 (-1)^n - 5)^6/64, {n, 1, 30}]
PROG
(Magma) /* By definition: */ k:=6; [n^k: n in [0..200] | Modexp(n, k, 10) eq k];
(Magma) [(10*n-3*(-1)^n-5)^6/64: n in [1..30]];
(PARI) vector(30, n, nn; (10*n-3*(-1)^n-5)^6/64)
(Sage) [(10*n-3*(-1)^n-5)^6/64 for n in (1..30)]
(Maxima) makelist((10*n-3*(-1)^n-5)^6/64, n, 1, 30);
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Bruno Berselli, May 24 2016
STATUS
approved