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A274603 Numbers n such that 2*n+1 and 3*n+1 are both triangular numbers. 5
45, 4455, 436590, 42781410, 4192141635, 410787098865, 40252943547180, 3944377680524820, 386508759747885225, 37873914077612227275, 3711257070846250387770, 363665319028854925774230, 35635490007756936475486815, 3491914355441150919671933685 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Inspired by A274579.
a(n+1) / a(n) goes to 49 + 20*sqrt(6) when n goes to infinity.
Intersection of A045943 and A074377. - Colin Barker, Jun 30 2016
LINKS
FORMULA
From Colin Barker, Jun 30 2016: (Start)
a(n) = 99*a(n-1)-99*a(n-2)+a(n-3) for n>3.
G.f.: 45*x / ((1-x)*(1-98*x+x^2)).
(End)
EXAMPLE
45 is a term because 2*45 + 1 = 91 and 3*45 + 1 = 136 are both triangular numbers.
PROG
(PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(3*n+1, 3);
(PARI) Vec(45*x/((1-x)*(1-98*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 30 2016
CROSSREFS
Sequence in context: A143004 A004707 A220094 * A036521 A328356 A093533
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Jun 30 2016
EXTENSIONS
More terms from Colin Barker, Jun 30 2016
STATUS
approved

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Last modified June 24 09:41 EDT 2024. Contains 373674 sequences. (Running on oeis4.)