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A098790
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Relates partial sums of Pell numbers with (P(n)+P(n-1)+1).
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1
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1, 2, 6, 15, 37, 90, 218, 527, 1273, 3074, 7422, 17919, 43261, 104442, 252146, 608735, 1469617, 3547970, 8565558, 20679087, 49923733, 120526554, 290976842, 702480239, 1695937321, 4094354882, 9884647086, 23863649055, 57611945197
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n+1) = - A024537(n+1) + 2*A048739(n+1) - 2*A048739(n); a(n) = - A024537(n) + A052542(n+1)
Partial sums of A074323. - Paul Barry (pbarry(AT)wit.ie), Mar 11 2007
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REFERENCES
| M. Bicknell, A Primer on the Pell Sequence and related sequences, Fibonacci Quarterly, Vol. 13, No. 4, 1975, pp. 345-349.
M. Bicknell-Johnson and G. E. Bergum, The Generalized Fibonacci Numbers {C(n)}, C(n)=C(n-1)+C(n-2)+K, Applications of Fibonacci Numbers, 1986, pp. 193-205.
A. F. Horadam, Special Properties of the Sequence W(n){a, b; p, q}, Fibonacci Quarterly, Vol. 5, No. 5, 1967, pp. 424-434.
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FORMULA
| a(n) = 2*a(n-1) + a(n-2) + 1, a(0) = 1, a(1) = 2; G.f. (x^2-x+1)/((1-x)(1-2x-x^2))
a(n)=(sqrt(2)+1)^n*(3/4+sqrt(2)/4)+(sqrt(2)-1)^n*(3/4-sqrt(2)/4)*(-1)^n-1/2; - Paul Barry (pbarry(AT)wit.ie), Mar 11 2007
a(0)=1, a(1)=2, a(2)=6, a(n)=3*a(n-1)-a(n-2)-a(n-3) [From Harvey P. Dale, Oct 15 2011]
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MATHEMATICA
| a[0] = 1; a[1] = 2; a[n_] := a[n] = 2a[n - 1] + a[n - 2] + 1; Table[ a[n], {n, 0, 28}] (from Robert G. Wilson v Nov 04 2004)
LinearRecurrence[{3, -1, -1}, {1, 2, 6}, 31] (* From Harvey P. Dale, Oct 15 2011 *)
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PROG
| Floretion Algebra Multiplication Program, FAMP
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CROSSREFS
| Cf. A048739, A024537.
Sequence in context: A018018 A030009 A061261 * A018019 A034518 A106515
Adjacent sequences: A098787 A098788 A098789 * A098791 A098792 A098793
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KEYWORD
| nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 30 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2004
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