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
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).
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
Comments