A380820 a(0) = 0, a(1) = 1, and for n >= 2, a(n) = a(n-1) + a(n-2) if a(n-1) < n, otherwise a(n-1) - n.

0, 1, 1, 2, 3, 5, 8, 1, 9, 0, 9, 9, 18, 5, 23, 8, 31, 14, 45, 26, 6, 32, 10, 42, 18, 60, 34, 7, 41, 12, 53, 22, 75, 42, 8, 50, 14, 64, 26, 90, 50, 9, 59, 16, 75, 30, 105, 58, 10, 68, 18, 86, 34, 120, 66, 11, 77, 20, 97, 38, 135, 74, 12, 86, 22, 108, 42, 150

Offset

0,4

Comments

Sequence starts with the first 7 Fibonacci numbers. For n >= 12, a(n) takes the values of (8*n+30)/7, (n+22)/7, (9*n+35)/7, (2*n+26)/7, (11*n+41)/7, (4*n+30)/7, and (15*n+45)/7 sequentially for n = 5, 6, 0, 1, 2, 3, 4 mod 7 (see plot in Links), which correspond to A017089 (n>=2), A000027 (n>=5), A017221 (n>=2), A005843 (n>=4), A017497 (n>=2), A016825 (n>=3), and A008597 (n>=3), respectively.

Terms for n >= 16 are the same as A322558(n) for n >= 17.

Links

Table of n, a(n) for n=0..67.

Ya-Ping Lu, Plot of A380820

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,2,0,0,0,0,0,0,-1).

Formula

a(n) = A322558(n+1) for n >= 16.

Mathematica

s={0, 1}; Do[AppendTo[s, If[s[[-1]]<n, s[[-1]]+s[[-2]], s[[-1]]-n]], {n, 2, 67}]; s (* James C. McMahon, Feb 14 2025 *)

Prog

(Python) def A380820(n): R = [0, 1, 1, 2, 3, 5, 8, 1, 9, 0, 9, 9]; X = [9, 2, 11, 4, 15, 8, 1]; Y = [35, 26, 41, 30, 45, 30, 22]; return R[n] if n < 12 else (X[n%7]*n + Y[n%7])//7

Crossrefs

Cf. A000027, A000045, A005843, A008597, A016825, A017089, A017221, A017497, A322558.

Sequence in context: A093086 A093092 A031111 * A089911 A098978 A111301

Adjacent sequences: A380816 A380818 A380819 * A380825 A380826 A380828

Keyword

nonn,easy,new

Author

Ya-Ping Lu, Feb 04 2025

Status

approved