OFFSET
1,1
COMMENTS
The definition of this sequence is inspired by the first 3+2+3+2 decimals of Pi, which have the property that 141+59=200, 265+35=300. The following 3+2 digits don't share such a property, but are followed by digits 238,462 with sum 700... - M. F. Hasler, May 01 2008
Using the given formula for a(n) we could construct d(n)= sum(k=1,n,(81 - (37*(-1)^k)*k + 2*(-1)^k + 25*k)/10^(1/4-1/4*(-1)^k+5/2*k)).
E.g. sum(k=1,6,(81 + (37*(-1)^(k+1) + 25)*k + 2*(-1)^k)/10^(1/4*(1 + (-1)^(k+1) + 10*k))) = 0.141592653538911 and sum(k=1..oo,(81 - (37*(-1)^k)*k + 2*(-1)^k + 25*k)/10^(1/4-1/4*(-1)^k+5/2*k)) = 0.1415926535389115128763663759...
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: (22*x^9 + 26*x^7 - 83*x^5 - 17*x^4 - 24*x^3 + 124*x^2 + 59*x +141) /(x^6 -x^4 - x^2 + 1).
a(n) = a(n-2) + a(n-4) - a(n-6).
a(n) = 81 - 37*(-1)^n*n + 2*(-1)^n + 25*n.
MATHEMATICA
CoefficientList[Series[(22*x^9 + 26*x^7 - 83*x^5 - 17*x^4 - 24*x^3 + 124*x^2 + 59*x + 141)/(x^6 - x^4 - x^2 + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 21 2017 *)
PROG
(PARI) a(n) = {local(a = vector(n)); a[1]=141; a[2]=59; for(m=3, n, if((Mod(m, 2))==0, a[m]=abs(a[m-3]+a[m-2]+100-a[m-1])); if((Mod(m, 2))!=0, a[m]=a[m-2]+124; ); ); a; }
(PARI) A137506(n)=if( n%2, 141+n\2*124, if( n<6, [59, 35][n\2], [11, 13][1+!(n%4)])) \\ M. F. Hasler, May 01 2008
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alexander R. Povolotsky, Apr 23 2008
EXTENSIONS
Edited & extended by M. F. Hasler, May 01 2008
STATUS
approved