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 A022107 Fibonacci sequence beginning 1, 17. 2
 1, 17, 18, 35, 53, 88, 141, 229, 370, 599, 969, 1568, 2537, 4105, 6642, 10747, 17389, 28136, 45525, 73661, 119186, 192847, 312033, 504880, 816913, 1321793, 2138706, 3460499, 5599205, 9059704, 14658909 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n-1)=sum(P(17;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=16. These are the SW-NE diagonals in P(17;n,k), the (17,1) 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)=17. a(-1):=16. G.f.: (1+16*x)/(1-x-x^2). a(n) = 17*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(17*fibonacci(n)+fibonacci(n-1)); od; end: P(30); # Paolo P. Lava, May 19 2015 MATHEMATICA a={}; b=1; c=17; 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, 17}, 40] (* Harvey P. Dale, Aug 04 2017 *) PROG (MAGMA) a0:=1; a1:=17; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013 CROSSREFS a(n) = A109754(16, n+1) = A101220(16, 0, n+1). Sequence in context: A242975 A155561 A231505 * A041584 A041586 A041588 Adjacent sequences:  A022104 A022105 A022106 * A022108 A022109 A022110 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 16 05:44 EDT 2018. Contains 316259 sequences. (Running on oeis4.)