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

Author

José María Grau Ribas, Jan 20 2016

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000045, A267806, A267807, A267808.

Programs

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

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

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 *)

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

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