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A117585 a(n) = 2*(a(n-1))+ a(n-2) + n. 1
1, 3, 9, 24, 61, 151, 369, 896, 2169, 5243, 12665, 30584, 73845, 178287, 430433, 1039168, 2508785, 6056755, 14622313, 35301400, 85225133, 205751687, 496728529, 1199208768, 2895146089, 6989500971, 16874148057, 40737797112, 98349742309 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A modified Pellian sequence.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4,0,1).

FORMULA

a(n)/a(n-1) tends to 1 + sqrt(2) = 2.414213562...(a(14)/a(13) = 430433/178287 = 2.4142702...).

(1/2) [Pell(n+1) + 2*Pell(n) - n - 2 ], with Pell(n) = A000129(n). - Ralf Stephan, May 15 2007

a(n)=4*a(n-1)-4*a(n-2)+a(n-4). G.f.: -(1-x+x^2)/((x^2+2*x-1)*(x-1)^2). [From R. J. Mathar, Aug 05 2009]

EXAMPLE

a(4) = 61 = 2*(a(3)) + a(2) + 4 = 2*24 + 9 + 4.

a(4) = 61 = sum of terms in row 5 of A117584: 1 + 5 + 9 + 17 + 29.

MATHEMATICA

RecurrenceTable[{a[0]==1, a[1]==3, a[n]==2a[n-1]+a[n-2]+n}, a, {n, 30}] (* or *) LinearRecurrence[{4, -4, 0, 1}, {1, 3, 9, 24}, 30] (* Harvey P. Dale, Mar 11 2015 *)

CROSSREFS

Row sums of triangle A117584.

Sequence in context: A003262 A189162 A079282 * A317474 A279978 A269601

Adjacent sequences:  A117582 A117583 A117584 * A117586 A117587 A117588

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Mar 29 2006

EXTENSIONS

Terms from a(20) on corrected by R. J. Mathar, Aug 05 2009

STATUS

approved

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Last modified September 20 18:52 EDT 2019. Contains 327245 sequences. (Running on oeis4.)