A153285 a(1)=1; for n > 1, a(n) = n^2 + Sum_{j=1..n-1} (-1)^j*a(j).

1, 3, 11, 7, 23, 11, 35, 15, 47, 19, 59, 23, 71, 27, 83, 31, 95, 35, 107, 39, 119, 43, 131, 47, 143, 51, 155, 55, 167, 59, 179, 63, 191, 67, 203, 71, 215, 75, 227, 79, 239, 83, 251, 87, 263, 91, 275, 95, 287, 99, 299, 103, 311, 107, 323, 111, 335, 115, 347, 119, 359

Offset: 1

Author

Walter Carlini, Dec 23 2008

Keywords

• nonn
• easy

Comments

1 followed by interleaving of A004767 and A017653. - Klaus Brockhaus, Jan 04 2009

Examples

			a(1) = 1;
a(2) = 2^2 - a(1) = 4 - 1 = 3;
a(3) = 3^2 + a(2) - a(1) = 9 + 3 - 1 = 11;
a(4) = 4^2 - 11 + 3 - 1 = 7;
a(5) = 25 + 7 - 11 + 3 - 1 = 23;
a(6) = 36 - 23 + 7 - 11 + 3 - 1 = 11; etc.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

The second of a family of sequences that includes A153284 and A153286

Cf. A004767 (4n+3), A017653 (12n+11). - Klaus Brockhaus, Jan 04 2009

Programs

Magma

S:=[ 1 ]; for n in [2..61] do Append(~S, n^2 + &+[ (-1)^j*S[j]: j in [1..n-1] ]); end for; S; // Klaus Brockhaus, Jan 04 2009

Scheme

(define (A153285 n) (cond ((= 1 n) n) ((even? n) (+ n n -1)) (else (+ (* 6 n) -7)))) ;; Antti Karttunen, Aug 10 2017

Formula

a(n) = 2n-1 if n is 1 or an even number;

a(n) = 6n-7 if n is an odd number other than 1.

G.f.: x*(1 + 3*x + 9*x^2 + x^3 + 2*x^4)/((1+x)^2*(1-x)^2). - Klaus Brockhaus, Oct 15 2009

a(n) = 4*(n-1) - (2*n-3)*(-1)^n for n>1, a(1)=1. - Bruno Berselli, Sep 14 2011

Extensions

Extended beyond a(30) by Klaus Brockhaus, Jan 04 2009