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%I #30 Jan 31 2021 20:24:33
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,13,25,49,97,193,385,769,1537,3073,6145,
%T 12289,24577,49153,98305,196597,393169,786289,1572481,3144769,6289153,
%U 12577537,25153537,50304001,100601857,201191425,402358273,804667393
%N 13th-order Fibonacci numbers: a(n) = a(n-1) + ... + a(n-13) with a(1)=...=a(13)=1.
%H Harvey P. Dale, <a href="/A163551/b163551.txt">Table of n, a(n) for n = 1..1000</a>
%H Kai Wang, <a href="https://www.researchgate.net/publication/344295426_IDENTITIES_FOR_GENERALIZED_ENNEANACCI_NUMBERS">Identities for generalized enneanacci numbers</a>, Generalized Fibonacci Sequences (2020).
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1,1,1,1,1).
%F a(n) = a(n-1)+a(n-2)+...+a(n-13) for n > 12, a(0)=a(1)=...=a(12)=1.
%F G.f.: (-1)*(-1+x^2+2*x^3+3*x^4+4*x^5+5*x^6+6*x^7+7*x^8+8*x^9+9*x^10 +10*x^11 +11*x^12) / (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13). - _Michael Burkhart_, Feb 18 2012
%t With[{c=Table[1,{13}]},LinearRecurrence[c,c,40]] (* _Harvey P. Dale_, Aug 09 2013 *)
%o (PARI) x='x+O('x^50); Vec((1-x^2 -2*x^3-3*x^4 -4*x^5-5*x^6 -6*x^7-7*x^8 -8*x^9 -9*x^10 -10*x^11 -11*x^12) / (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13)) \\ _G. C. Greubel_, Jul 28 2017
%Y Cf. A000045 (Fibonacci numbers), A000213 (tribonacci), A000288 (tetranacci), A000322 (pentanacci), A000383 (hexanacci), A060455 (heptanacci), A123526 (octanacci), A127193 (nonanacci), A127194 (decanacci), A127624 (undecanacci), A207539 (dodecanacci).
%K nonn,easy
%O 1,14
%A Jainit Purohit (mjainit(AT)gmail.com), Jul 30 2009
%E Values adapted to the definition by _R. J. Mathar_, Aug 01 2009
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