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A111649 a(n) = A001541(n)*A001653(n+1) + A001541(n)*A002315(n) + A001653(n+1)*A002315(n). 3
3, 71, 2379, 80783, 2744211, 93222359, 3166815963, 107578520351, 3654502875939, 124145519261543, 4217293152016491, 143263821649299119, 4866752642924153523, 165326326037771920631, 5616228332641321147899 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
a(n) = A001653(2n+2) - 2*A002315(n)^2, e.g., 2379 = 5741 - 2*41^2;
a(n) = A001652(2n) + A002315(n)^2 + 2, e.g., 2379 = 696 + 41^2 + 2;
a(n) = 2*A046176(n+1)+1, e.g., 2379 = 2*1189 + 1.
G.f.: (x^2+34*x-3) / ((x-1)*(x^2-34*x+1)). - Colin Barker, Dec 14 2014 [adjusted for corrected term and empirical g.f. confirmed for more terms and recurrence of source sequences. - Ray Chandler, Feb 05 2024]
EXAMPLE
a(1) = 71 = 3*5 + 3*7 + 5*7.
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {3, 71, 2379}, 20] (* Paolo Xausa, Feb 06 2024 *)
CROSSREFS
Sequence in context: A166449 A094458 A183548 * A349072 A272657 A226709
KEYWORD
nonn
AUTHOR
Charlie Marion, Aug 24 2005
EXTENSIONS
a(3) = 80783 corrected by Ray Chandler, Feb 05 2024
STATUS
approved

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Last modified April 23 09:48 EDT 2024. Contains 371905 sequences. (Running on oeis4.)