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A001932
Sum of Fibonacci (A000045) and Pell (A000129) numbers.
(Formerly M0844 N0319)
2
0, 2, 3, 7, 15, 34, 78, 182, 429, 1019, 2433, 5830, 14004, 33694, 81159, 195635, 471819, 1138286, 2746794, 6629290, 16001193, 38624911, 93240069, 225087338, 543386088, 1311813146, 3166937355, 7645566463, 18457873863, 44560996378, 107579352390, 259718869118
OFFSET
0,2
COMMENTS
In general, the sum of two Horadam sequences having signatures of (a,b) and (c,d) will be a fourth-order sequence with signature (a+c,d-a*c+b,-a*d-b*c,-b*d). - Gary Detlefs, Oct 13 2020
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Eric Weisstein's World of Mathematics, Horadam Sequence.
MAPLE
gfpell := x/(1-2*x-x^2): gffib := x/(1-x-x^2): s := series(gfpell+gffib, x, 100): for i from 1 to 60 do printf(`%d, `, coeff(s, x, i)) od:
A001932:=-(z+2)*(2*z-1)/(z**2+z-1)/(z**2+2*z-1); # Conjectured (correctly) by Simon Plouffe in his 1992 dissertation
with (combinat):seq(sum((fibonacci(n, m)), m=1..2), n=1..30); # Zerinvary Lajos, Jun 19 2008
MATHEMATICA
nn = 30; CoefficientList[Series[-x*(x + 2)*(2*x - 1)/(x^2 + x - 1)/(x^2 + 2*x - 1), {x, 0, nn}], x] (* T. D. Noe, Aug 17 2012 *)
LinearRecurrence[{3, 0, -3, -1}, {0, 2, 3, 7}, 30] (* T. D. Noe, Apr 16 2013 *)
CROSSREFS
Sequence in context: A368410 A358734 A198683 * A213920 A248869 A005909
KEYWORD
nonn,easy
EXTENSIONS
More terms from James A. Sellers, Apr 06 2001
STATUS
approved