A267809 a(1)=a(2)=1; if n>2 then a(n) = a(n-2) + (a(n-1) mod 10).

1, 1, 2, 3, 5, 8, 13, 11, 14, 15, 19, 24, 23, 27, 30, 27, 37, 34, 41, 35, 46, 41, 47, 48, 55, 53, 58, 61, 59, 70, 59, 79, 68, 87, 75, 92, 77, 99, 86, 105, 91, 106, 97, 113, 100, 113, 103, 116, 109, 125, 114, 129, 123, 132, 125, 137, 132, 139, 141, 140, 141, 141, 142, 143, 145, 148, 153

Offset

1,3

Comments

a(n) - (7/3)*n is periodic with period 60. - Robert Israel, Jan 20 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

Formula

G.f.: (x + x^2 + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 7*x^7 + 2*x^8 + 2*x^10 + 2*x^11 + 4*x^12 - 3*x^13 + x^14 + 7*x^15 - 3*x^16 + 4*x^17 + 2*x^18 + 5*x^19 - 3*x^20 - 7*x^21 + x^22 - 6*x^23 + 4*x^24 - x^25 + 3*x^26 + x^27 + 3*x^28 + 4*x^29 - 2*x^30 + 2*x^31 + 2*x^33 + 3*x^34 + 5*x^35 + 7*x^36 + 2*x^37 + 9*x^38 + x^39 - x^40)/(1 - x^2 - x^6 + x^8 + x^12 - x^14 - x^15 + x^17 - x^18 + x^20 + x^21 - x^23 + x^24 - x^26 - x^27 + x^29 + x^33 - x^35 - x^39 + x^41). - Robert Israel, Jan 20 2016

Maple

A[1]:=1: A[2]:= 1:
for n from 3 to 100 do A[n]:= A[n-2] + (A[n-1] mod 10) od:
seq(A[n], n=1..100); # Robert Israel, Jan 20 2016

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = Mod[a[n - 1], 10] + a[n - 2]; Array[a, 100]
nxt[{n_, a_, b_}]:={n+1, b, a+Mod[b, 10]}; NestList[nxt, {2, 1, 1}, 70] [[All, 2]] (* Harvey P. Dale, Nov 13 2021 *)

Prog

(PARI) lista(nn)=print1(a = 1, ", "); print1(b = 1, ", "); for (n=1, nn, c = a + b % 10; print1(c, ", "); a = b; b = c; ); \\ Michel Marcus, Feb 10 2016
(PARI) a=vector(10^5); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-1]%10+a[n-2]); a \\ Altug Alkan, Mar 20 2018
(Magma) I:=[1, 1, 2]; [n le 3 select I[n] else Self(n-2)+(Self(n-1)mod 10): n in [1..70]]; // Vincenzo Librandi, Feb 12 2016
(GAP) a:=[1, 1];; for n in [3..70] do a[n]:=a[n-2]+(a[n-1] mod 10); od; a; # Muniru A Asiru, Mar 20 2018

Crossrefs

Cf. A000045, A267806, A267807, A267808.

Sequence in context: A300999 A074867 A131297 * A010077 A364120 A065076

Adjacent sequences: A267806 A267807 A267808 * A267810 A267811 A267812

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 20 2016

Status

approved