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A084637 Binomial transform of (1,0,1,0,1,0,1,1,1,1,1,....). 3
1, 1, 2, 4, 8, 16, 32, 65, 136, 293, 642, 1410, 3072, 6606, 14004, 29295, 60592, 124187, 252742, 511672, 1031912, 2075452, 4166408, 8353165, 16732664, 33498977, 67040458, 134134046, 268333872, 536748474, 1073595228, 2147309211, 4294760928, 8589691767 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence starting 1,2,4,... is the binomial transform of (1,1,1,1,1,1,2,2,2...) with a(n) = sum{k=0..5, C(n,k)} + 2*sum{k=6..n, C(n,k)} = 2^n-(n^5-5*n^4+25*n^3+5*n^2+94*n+120)/120. This gives the partial sums of A084636.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-27,50,-55,36,-13,2)

FORMULA

a(n) = sum{k=0..2, C(n, 2*k)} + sum{k=6..n, C(n, k)};

a(n) = 2^n-n(n^4-10*n^3+55*n^2-110*n+184)/120.

G.f.: (1-7*x+21*x^2-35*x^3+35*x^4-21*x^5+7*x^6) / ((1-x)^6*(1-2*x)). - Colin Barker, Mar 17 2016

PROG

(PARI) Vec((1-7*x+21*x^2-35*x^3+35*x^4-21*x^5+7*x^6)/((1-x)^6*(1-2*x)) + O(x^50)) \\ Colin Barker, Mar 17 2016

CROSSREFS

Cf. A084634, A000325, A000225.

Sequence in context: A101333 A023421 A098051 * A100137 A210542 A141366

Adjacent sequences:  A084634 A084635 A084636 * A084638 A084639 A084640

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 06 2003

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)