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A184418 Convolution square of A040001. 2
1, 2, 5, 6, 10, 10, 15, 14, 20, 18, 25, 22, 30, 26, 35, 30, 40, 34, 45, 38, 50, 42, 55, 46, 60, 50, 65, 54, 70, 58, 75, 62, 80, 66, 85, 70, 90, 74, 95, 78, 100, 82, 105, 86, 110, 90, 115, 94, 120, 98, 125, 102, 130, 106, 135, 110, 140, 114, 145, 118, 150, 122, 155, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Michael Somos, Rational Function Multiplicative Coefficients

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

G.f.: (1 + x + x^2)^2 / (1 - x^2)^2 = 1 + x * (x + 2) * (2*x + 1) / (1 - x^2)^2. a(-n) = -a(n) except a(0) = 2.

Euler transform of length 3 sequence [2, 2, -2].

a(n) = 2 * b(n) where b() is multiplicative with b(2^e) = 5 * 2^(e-2) if e>0, b(p^e) = p^e if p>2.

a(2*n + 1) = 4*n + 2, a(2*n) = 5*n except a(0) = 2.

a(n) = (9+(-1)^n)*n/4 = (n/2)*A010710(n+1) for n>0. - Bruno Berselli, Mar 24 2011

EXAMPLE

G.f. = 1 + 2*x + 5*x^2 + 6*x^3 + 10*x^4 + 10*x^5 + 15*x^6 + 14*x^7 + 20*x^8 + ...

MATHEMATICA

LinearRecurrence[{0, 2, 0, -1}, {1, 2, 5, 6, 10}, 80] (* Harvey P. Dale, Jul 03 2017 *)

PROG

(PARI) {a(n) = (n==0) + n * ([5/2, 2] [n%2 + 1])};

(PARI) {a(n) = if( n==0, 1, sign(n) * polcoeff( (1 + x + x^2)^2 / (1 - x^2)^2 + x * O(x^abs(n)), abs(n)))};

(Magma) I:=[2, 5, 6, 10]; [1] cat [n le 4 select I[n] else 2*Self(n-2) - Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 14 2018

CROSSREFS

Sequence in context: A295741 A007503 A337298 * A112967 A244731 A307562

Adjacent sequences: A184415 A184416 A184417 * A184419 A184420 A184421

KEYWORD

nonn

AUTHOR

Michael Somos, Feb 14 2011

STATUS

approved

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Last modified November 28 10:39 EST 2022. Contains 358411 sequences. (Running on oeis4.)