OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
From Colin Barker, Oct 21 2015: (Start)
a(n) = -5-(1/2+i)*(-i)^n-(1/2-i)*i^n+5*n for n>1, where i = sqrt(-1).
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>5.
G.f.: x*(5*x^4-4*x^3+6*x^2+3) / ((x-1)^2*(x^2+1)).
(End)
From Robert Israel, Oct 21 2015: (Start)
a(n) = a(n-4) + 20 for n >= 6.
a(4k) = 20 k - 6.
a(4k+1) = 20 k - 2 for k >= 1.
a(4k+2) = 20 k + 6.
a(4k+3) = 20 k + 12. (End)
EXAMPLE
26+6=32, 32+2=34.
MATHEMATICA
a[1] = 3; a[n_] := a[n] = a[n - 1] + Last@ IntegerDigits@ a[n - 1]; Array[a, {57}] (* Michael De Vlieger, Oct 21 2015 *)
NestList[#+Mod[#, 10]&, 3, 60] (* Harvey P. Dale, Dec 23 2023 *)
PROG
(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
(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
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Samantha Stones (devilsdaughter2000(AT)hotmail.com), Dec 25 2004
EXTENSIONS
Offset set to 1 by Colin Barker, Oct 21 2015
STATUS
approved