id:A097038 - OEIS Search Results

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A Jacobsthal variant.

+0
3

0, 1, 1, 5, 7, 21, 35, 85, 155, 341, 651, 1365, 2667, 5461, 10795, 21845, 43435, 87381, 174251, 349525, 698027, 1398101, 2794155, 5592405, 11180715, 22369621, 44731051, 89478485, 178940587, 357913941, 715795115, 1431655765, 2863245995 (list; graph; listen)

	OFFSET	`0,4`
	COMMENT	`Convolution of A001045 and A077957. Also interleaving of A002450(n+1) and A006095(n+1).`
	FORMULA	`G.f. : 1/(1-x-2x^2)-1/(1-2x^2)=x/((1-2x^2)(1-x-2x^2)); a(n)=2*2^n/3+(-1)^n/3-2^(n/2)(1+(-1)^n)/2; a(n)=sum{k=0..floor((n+1)/2), binomial(n-k+1, k-1)2^k }; a(n)=sum{k=0..n, 2^(k/2)(1+(-1)^k)A001045(n-k)/2 }; a(n)=A001045(n+1)-A077957(n).`
	CROSSREFS	`Sequence in context: A076197 A002596 A098597 this_sequence A049114 A030735 A162462` `Adjacent sequences: A097035 A097036 A097037 this_sequence A097039 A097040 A097041`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Jul 19 2004`

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Last modified December 15 00:47 EST 2009. Contains 170825 sequences.

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