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A267809
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a(1)=a(2)=1; if n>2 then a(n) = a(n-2) + (a(n-1) mod 10).
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5
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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
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OFFSET
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1,3
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COMMENTS
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a(n) - (7/3)*n is periodic with period 60. - Robert Israel, Jan 20 2016
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LINKS
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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).
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FORMULA
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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
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MAPLE
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A[1]:=1: A[2]:= 1:
for n from 3 to 100 do A[n]:= A[n-2] + (A[n-1] mod 10) od:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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