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 A084638 Binomial transform of (1,0,1,0,1,0,1,0,2,0,2,0,2,....). 1
 1, 1, 2, 4, 8, 16, 32, 64, 129, 265, 558, 1200, 2610, 5682, 12288, 26292, 55587, 116179, 240366, 493108, 1004780, 2036692, 4112144, 8278552, 16631717, 33364381, 66863358, 133903816, 268037862, 536371734, 1073120208, 2146715436, 4294024647, 8588785575 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The sequence starting 1,2,4,... is the binomial transform of (1,1,1,1,1,1,1,2,2...) with a(n) = Sum_{k=0..6, C(n,k)} + 2*Sum_{k=7..n, C(n,k)} = 2^(n+1)-A008859(n). This gives the partial sums of A084637. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-35,77,-105,91,-49,15,-2). FORMULA a(n) = Sum_{k=0..3, C(n, 2*k)} + 2*Sum_{k=4..floor(n/2), C(n, 2*k)}. a(n) = (n^6-15*n^5+115*n^4-405*n^3+964*n^2-660*n+720)/720 + 2*Sum_{k=4..floor(n/2), C(n, 2k)}. G.f.: (1-8*x+28*x^2-56*x^3+70*x^4-56*x^5+28*x^6-8*x^7+2*x^8) / ((1-x)^7*(1-2*x)). - Colin Barker, Mar 17 2016 PROG (PARI) Vec((1-8*x+28*x^2-56*x^3+70*x^4-56*x^5+28*x^6-8*x^7+2*x^8)/((1-x)^7*(1-2*x)) + O(x^50)) \\ Colin Barker, Mar 17 2016 CROSSREFS Cf. A084634, A084635, A084636, A000325, A000225. Sequence in context: A117302 A265407 A023422 * A157021 A210543 A006211 Adjacent sequences:  A084635 A084636 A084637 * A084639 A084640 A084641 KEYWORD easy,nonn AUTHOR Paul Barry, Jun 06 2003 STATUS approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)