A259156
Positive triangular numbers (A000217) that are pentagonal numbers (A000326) divided by 2.
Original entry on oeis.org
6, 105, 58311, 1008910, 559902916, 9687554415, 5376187741821, 93019896484620, 51622154137063026, 893177036357767525, 495675918647891434531, 8576285810087387291130, 4759480119234899417304336, 82349495455282056411663435, 45700527609217585557064800441
Offset: 1
6 is in the sequence because 6 is the 3rd triangular number, and 2*6 is the 3rd pentagonal number.
-
LinearRecurrence[{1, 9602, -9602, -1, 1}, {6, 105, 58311, 1008910, 559902916}, 20] (* Vincenzo Librandi, Jun 20 2015 *)
-
Vec(-x*(x^3+594*x^2+99*x+6)/((x-1)*(x^2-98*x+1)*(x^2+98*x+1)) + O(x^20))
A259162
Positive hexagonal numbers (A000384) that are pentagonal numbers (A000326) divided by 2.
Original entry on oeis.org
6, 58311, 559902916, 5376187741821, 51622154137063026, 495675918647891434531, 4759480119234899417304336, 45700527609217585557064800441, 438816461344227137284036796530846, 4213515616126741362983735763224383551, 40458176507232509223142693514443734326556
Offset: 1
6 is in the sequence because 6 is the 2nd hexagonal number, and 2*6 is the 3rd pentagonal number.
-
LinearRecurrence[{9603, -9603, 1}, {6, 58311, 559902916}, 20] (* Vincenzo Librandi, Jun 20 2015 *)
-
Vec(-x*(x^2+693*x+6)/((x-1)*(x^2-9602*x+1)) + O(x^20))
A259165
Positive heptagonal numbers (A000566) that are pentagonal numbers (A000326) divided by 2.
Original entry on oeis.org
540, 125482435, 29152330292086, 6772727677992549813, 1573453639577432827392256, 365547896447135621647431177175, 84924818396817988252797073116286650, 19729903659220000770419185998874515952681, 4583690677832384200588508141377728222042497188
Offset: 1
540 is in the sequence because 540 is the 15th heptagonal number, and 2*540 is the 27th pentagonal number.
-
LinearRecurrence[{232323, -232323, 1}, {540, 125482435, 29152330292086}, 20] (* Vincenzo Librandi, Jun 20 2015 *)
-
Vec(-x*(x^2+28015*x+540)/((x-1)*(x^2-232322*x+1)) + O(x^20))
Showing 1-3 of 3 results.
Comments