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URL: https://oeis.org/A321421

⇱ A321421 - OEIS

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A321421
a(n) = 10*(4^n - 1)/3 + 1.
2
1, 11, 51, 211, 851, 3411, 13651, 54611, 218451, 873811, 3495251, 13981011, 55924051, 223696211, 894784851, 3579139411, 14316557651, 57266230611, 229064922451, 916259689811, 3665038759251, 14660155037011, 58640620148051, 234562480592211, 938249922368851
OFFSET
0,2
FORMULA
a(n) = 4*a(n-1) + 7, a(0) = 1 for n > 0.
a(n) = 5*a(n-1) - 4*a(n-2), a(0) = 1, a(1) = 11, n > 1.
a(n) = a(n-1) + 10*4^(n-1), a(0) = 1, n > 0.
a(n) = A086462(n) + 1 for n > 0. - Michel Marcus, Nov 09 2018
G.f.: (1 + 6*x) / ((1 - x)*(1 - 4*x)). - Colin Barker, Nov 10 2018
E.g.f.: (-7*exp(x) + 10*exp(4*x))/3. - Stefano Spezia, Nov 10 2018
a(n) = 10*A002450(n) + 1. - Omar E. Pol, Nov 10 2018
MAPLE
seq(coeff(series((1+6*x)/((1-x)*(1-4*x)), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Nov 10 2018
MATHEMATICA
a[n_]:=10*(4^n - 1)/3 + 1 ; Array[a, 20, 0] (* or *)
CoefficientList[Series[-((7 E^x)/3) + (10 E^(4 x))/3 , {x, 0, 20}], x]*Table[n!, {n, 0, 20}] (* Stefano Spezia, Nov 10 2018 *)
LinearRecurrence[{5, -4}, {1, 11}, 30] (* Harvey P. Dale, Aug 22 2020 *)
PROG
(PARI) Vec((1 + 6*x) / ((1 - x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Nov 10 2018
(GAP) List([0..25], n->10*(4^n-1)/3+1); # Muniru A Asiru, Nov 10 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 09 2018
EXTENSIONS
More terms from Colin Barker, Nov 10 2018
STATUS
approved