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 A022105 Fibonacci sequence beginning 1, 15. 2
 1, 15, 16, 31, 47, 78, 125, 203, 328, 531, 859, 1390, 2249, 3639, 5888, 9527, 15415, 24942, 40357, 65299, 105656, 170955, 276611, 447566, 724177, 1171743, 1895920, 3067663, 4963583, 8031246, 12994829 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n-1)=sum(P(15;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=14. These are the SW-NE diagonals in P(15;n,k), the (15,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs. LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (1,1) FORMULA a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=15. a(-1):=14. G.f.: (1+14*x)/(1-x-x^2). a(n) = A101220(14,0,n+1). - Ross La Haye, May 02 2006 a(n) = 15*A000045(n) + A000045(n-1). [Paolo P. Lava, May 19 2015] MAPLE with(numtheory): with(combinat): P:=proc(q) local n; for n from 0 to q do print(15*fibonacci(n)+fibonacci(n-1)); od; end: P(30); # Paolo P. Lava, May 19 2015 MATHEMATICA a={}; b=1; c=15; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *) LinearRecurrence[{1, 1}, {1, 15}, 40] (* Harvey P. Dale, Oct 11 2015 *) PROG (MAGMA) a0:=1; a1:=15; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013 CROSSREFS a(n) = A109754(14, n+1). a(k) = A118654(4, k). Sequence in context: A193566 A079832 A037971 * A041456 A041458 A041454 Adjacent sequences:  A022102 A022103 A022104 * A022106 A022107 A022108 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 10 13:02 EST 2018. Contains 318048 sequences. (Running on oeis4.)