OFFSET
0,2
LINKS
Iain Fox, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (26,-227,778,-840).
FORMULA
a(n) = -4*2^n/75 + 125*5^n/42 - 343*7^n/50 + 864*12^n/175. - R. J. Mathar, Jun 20 2013
a(n) = 26*a(n-1) - 227*a(n-2) + 778*a(n-3) - 840*a(n-4). - Iain Fox, Oct 19 2018
E.g.f.: (-56*exp(2*x) + 3125*exp(5*x) - 7203*exp(7*x) + 5184*exp(12*x)) / 1050. - G. C. Greubel, Oct 19 2018
MAPLE
seq(coeff(series(((1-2*x)*(1-5*x)*(1-7*x)*(1-12*x))^(-1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 19 2018
MATHEMATICA
Table[(-7*2^(3+n) +5^(5+n) -3*7^(4+n) +3*12^(3+n))/1050, {n, 0, 30}] (* G. C. Greubel, Oct 19 2018 *)
LinearRecurrence[{26, -227, 778, -840}, {1, 26, 449, 6550}, 20] (* Harvey P. Dale, May 28 2019 *)
PROG
(PARI) first(n) = Vec(1/((1-2*x)*(1-5*x)*(1-7*x)*(1-12*x)) + O(x^n)) \\ Iain Fox, Oct 19 2018
(PARI) a(n) = -4*2^n/75 + 125*5^n/42 - 343*7^n/50 + 864*12^n/175 \\ Iain Fox, Oct 19 2018
(Magma) [(-7*2^(3+n) +5^(5+n) -3*7^(4+n) +3*12^(3+n))/1050: n in [0..30]]; // G. C. Greubel, Oct 19 2018
(GAP) a:=[1, 26, 449, 6550];; for n in [5..20] do a[n]:=26*a[n-1]-227*a[n-2]+778*a[n-3]-840*a[n-4]; od; a; # Muniru A Asiru, Oct 19 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved