A102040 - OEIS

%I #30 Feb 23 2024 07:33:37

%S 3,6,12,14,18,26,32,34,38,46,52,54,58,66,72,74,78,86,92,94,98,106,112,

%T 114,118,126,132,134,138,146,152,154,158,166,172,174,178,186,192,194,

%U 198,206,212,214,218,226,232,234,238,246,252,254,258,266,272,274,278

%N a(n) = a(n-1) + last digit of a(n-1), starting at 3.

%H Colin Barker, <a href="/A102040/b102040.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).

%F From _Colin Barker_, Oct 21 2015: (Start)

%F a(n) = -5-(1/2+i)*(-i)^n-(1/2-i)*i^n+5*n for n>1, where i = sqrt(-1).

%F a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>5.

%F G.f.: x*(5*x^4-4*x^3+6*x^2+3) / ((x-1)^2*(x^2+1)).

%F (End)

%F From _Robert Israel_, Oct 21 2015: (Start)

%F a(n) = a(n-4) + 20 for n >= 6.

%F a(4k)   = 20 k - 6.

%F a(4k+1) = 20 k - 2 for k >= 1.

%F a(4k+2) = 20 k + 6.

%F a(4k+3) = 20 k + 12. (End)

%e 26+6=32, 32+2=34.

%t a[1] = 3; a[n_] := a[n] = a[n - 1] + Last@ IntegerDigits@ a[n - 1]; Array[a, {57}] (* _Michael De Vlieger_, Oct 21 2015 *)

%t NestList[#+Mod[#,10]&,3,60] (* _Harvey P. Dale_, Dec 23 2023 *)

%o (PARI) a(n) = if(n==1, 3, -5-(1/2+I)*(-I)^n-(1/2-I)*I^n+5*n) \\ _Colin Barker_, Oct 21 2015

%o (PARI) Vec(x*(5*x^4-4*x^3+6*x^2+3)/((x-1)^2*(x^2+1)) + O(x^100)) \\ _Colin Barker_, Oct 21 2015

%K easy,nonn,base

%O 1,1

%A Samantha Stones (devilsdaughter2000(AT)hotmail.com), Dec 25 2004

%E Offset set to 1 by _Colin Barker_, Oct 21 2015