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A238846 Expansion of (1-2*x)/(1-3*x+x^2)^2. 3
1, 4, 13, 40, 120, 354, 1031, 2972, 8495, 24110, 68016, 190884, 533293, 1484020, 4115185, 11375764, 31358376, 86223942, 236540915, 647556620, 1769374931, 4826148314, 13142564448, 35736448200, 97037995225, 263156279524, 712795854421, 1928547574912, 5212430732760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of 1, 1, 2, 5, 13, ... (A001519(n)) with 1, 3, 8, 21, 55, ... (A001906(n+1)).

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

FORMULA

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4) for n>3, a(0)=1, a(1)=4, a(2)=13, a(3)=40.

a(n) = 3*a(n-1) - a(n-2) + A001519(n) for n>1, a(0)=1, a(1)=4.

a(n) = A238731(n+1, 1).

a(n) = -A124037(n+1, 1).

a(n) = (-1)^n*A126126(n+1, 1).

a(n) = ( (3 + sqrt(5))^(1+n)*(8 - (1 - sqrt(5))*(13 + 5*n)) + (3 - sqrt(5))^(1+n)*(8 - (1 + sqrt(5))*(13 + 5*n)) ) / (25*2^(2+n)). - Bruno Berselli, Mar 06 2014

a(n) = 2*A001870(n) - A001871(n). - Philippe Deléham, Mar 06 2014

a(n) = A197649(n+1) - 3*A001871(n-1). - Philippe Deléham, Mar 06 2014

a(n) = A001871(n) - 2*A001871(n-1). - Philippe Deléham, Mar 06 2014

EXAMPLE

a(0) = 1*1 = 1;

a(1) = 1*3 + 1*1 = 4;

a(2) = 1*8 + 1*3 + 2*1 = 13;

a(3) = 1*21 + 1*8 + 2*3 + 5*1 = 40;

a(4) = 1*55 + 1*21 + 2*8 + 5*3 + 13*1 = 120; etc (from first recurrence formula).

a(0) = 3*0 - 0 + 1 = 1;

a(1) = 3*1 - 0 + 1 = 4;

a(2) = 3*4 - 1 + 2 = 13;

a(3) = 3*13 - 4 + 5 = 40;

a(4) = 3*40 - 13 + 13 = 120; etc (from second recurrence formula).

MATHEMATICA

LinearRecurrence[{6, -11, 6, -1}, {1, 4, 13, 40}, 30] (* Bruno Berselli, Mar 06 2014 *)

CROSSREFS

Cf. A000045, A001519, A001906.

Cf. A001870, A001871, A197649.

Sequence in context: A137744 A027130 A027121 * A025567 A003462 A076040

Adjacent sequences:  A238843 A238844 A238845 * A238847 A238848 A238849

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Mar 05 2014

STATUS

approved

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)