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A081033
6th binomial transform of the periodic sequence (1,7,1,1,7,1...).
4
1, 13, 121, 997, 7729, 57853, 423721, 3059797, 21887329, 155555053, 1100604121, 7762822597, 54632726929, 383893932253, 2694581744521, 18898693305397, 132473958606529, 928233237589453, 6502210299844921, 45538360282508197, 318882962895526129, 2232752944858526653
OFFSET
0,2
FORMULA
a(n) = 7*a(n-1) + 6*5^(n-1).
a(n) = 4*7^n - 3*5^n.
G.f.: (1+x)/((1-5*x)*(1-7*x)). - Vincenzo Librandi, Aug 06 2013
E.g.f.: exp(5*x)*(4*exp(2*x) - 3). - Stefano Spezia, Jul 23 2024
MATHEMATICA
CoefficientList[Series[(1 + x) / ((1 - 5 x) (1 - 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{12, -35}, {1, 13}, 30] (* Harvey P. Dale, Aug 18 2015 *)
PROG
(Magma) [4*7^n-3*5^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
CROSSREFS
Sequence in context: A054962 A297394 A014918 * A091111 A196921 A317483
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 03 2003
STATUS
approved