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A139698
Binomial transform of [1, 25, 25, 25, ...].
7
1, 26, 76, 176, 376, 776, 1576, 3176, 6376, 12776, 25576, 51176, 102376, 204776, 409576, 819176, 1638376, 3276776, 6553576, 13107176, 26214376, 52428776, 104857576, 209715176, 419430376, 838860776, 1677721576, 3355443176, 6710886376, 13421772776, 26843545576
OFFSET
1,2
COMMENTS
The binomial transform of [1, c, c, c, ...] has the terms a(n)=1-c+c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar, May 11 2008
FORMULA
A007318 * [1, 25, 25, 25, ...].
a(n) = 25*2^(n-1)-24. - Emeric Deutsch, May 03 2008
a(n) = 2*a(n-1) + 24 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010
a(n) = 3*a(n-1)-2*a(n-2). G.f.: x*(23*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Mar 11 2014
EXAMPLE
a(3) = 76 = (1, 2, 1) dot (1, 25, 25) = (1 + 50 + 25).
MAPLE
seq(25*2^(n-1)-24, n=1..25); # Emeric Deutsch, May 03 2008
MATHEMATICA
LinearRecurrence[{3, -2}, {1, 26}, 40] (* Harvey P. Dale, Jul 25 2021 *)
PROG
(PARI) Vec(x*(23*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014
(Magma) [25*2^(n-1)-24 : n in [1..40]]; // Wesley Ivan Hurt, Jan 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 29 2008
EXTENSIONS
More terms from Emeric Deutsch, May 03 2008
More terms from Colin Barker, Mar 11 2014
STATUS
approved