A139579 -id:A139579 - cp's OEIS frontend

A139576 a(n) = n(2n + 9).

0, 11, 26, 45, 68, 95, 126, 161, 200, 243, 290, 341, 396, 455, 518, 585, 656, 731, 810, 893, 980, 1071, 1166, 1265, 1368, 1475, 1586, 1701, 1820, 1943, 2070, 2201, 2336, 2475, 2618, 2765, 2916, 3071, 3230, 3393, 3560, 3731, 3906

Offset: 0

Omar E. Pol, May 19 2008

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A014105, A014106, A033537, A130861, A139577, A139578, A139579, A139580, A139581.

Cf. A277979.

s=0;lst={s};Do[s+=n++ +11;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[Sum[(2*i + n - 1), {i, 4, n}], {n, 3, 45}] (* Zerinvary Lajos, Jul 11 2009 *)
Table[n(2n+9),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,11,26},50] (* Harvey P. Dale, Dec 18 2018 *)

a(n)=n*(2*n+9) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 9*n.
a(n) = a(n-1) + 4*n + 7 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(11 - 7*x)/(1-x)^3.
E.g.f.: exp(x)*x*(11 + 2*x).
a(n) = A277979(n)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139577 a(n) = n(2n + 11).

Original entry on oeis.org

0, 13, 30, 51, 76, 105, 138, 175, 216, 261, 310, 363, 420, 481, 546, 615, 688, 765, 846, 931, 1020, 1113, 1210, 1311, 1416, 1525, 1638, 1755, 1876, 2001, 2130, 2263, 2400, 2541, 2686, 2835, 2988, 3145, 3306, 3471, 3640, 3813, 3990

Offset: 0

Omar E. Pol, May 19 2008

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A014105, A014106, A033537, A130861, A139576, A139578, A139579, A139580, A139581.

s=0;lst={s};Do[s+=n++ +13;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[n(2n+11),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,30},50] (* Harvey P. Dale, Mar 17 2019 *)

a(n)=n*(2*n+11) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 11*n.
a(n) = a(n-1) + 4*n + 9 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(13 - 9*x)/(1-x)^3.
E.g.f.: exp(x)*x*(13 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139578 a(n) = n(2n + 13).

Original entry on oeis.org

0, 15, 34, 57, 84, 115, 150, 189, 232, 279, 330, 385, 444, 507, 574, 645, 720, 799, 882, 969, 1060, 1155, 1254, 1357, 1464, 1575, 1690, 1809, 1932, 2059, 2190, 2325, 2464, 2607, 2754, 2905, 3060, 3219, 3382, 3549, 3720, 3895, 4074, 4257, 4444, 4635, 4830, 5029

Offset: 0

Omar E. Pol, May 19 2008

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139579, A139580, A139581.

s=0;lst={s};Do[s+=n++ +15;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[n(2n+13),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,15,34},50] (* Harvey P. Dale, Nov 22 2014 *)

a(n)=n*(2*n+13) \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 2*n^2 + 13*n.
a(n) = a(n-1) + 4*n + 11 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(15 - 11*x)/(1 - x)^3.
E.g.f.: exp(x)*x*(15 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139580 a(n) = n(2n + 17).

Original entry on oeis.org

0, 19, 42, 69, 100, 135, 174, 217, 264, 315, 370, 429, 492, 559, 630, 705, 784, 867, 954, 1045, 1140, 1239, 1342, 1449, 1560, 1675, 1794, 1917, 2044, 2175, 2310, 2449, 2592, 2739, 2890, 3045, 3204, 3367, 3534, 3705, 3880, 4059

Offset: 0

Omar E. Pol, May 19 2008

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139579, A139581.

a[n_]:=Sum[4*i+15, {i, 1, n}]; (* Vladimir Joseph Stephan Orlovsky, Dec 04 2008 *)
Table[n(2n+17),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,19,42},50] (* Harvey P. Dale, Jul 07 2024 *)

a(n)=n*(2*n+17) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 17*n.
a(n) = a(n-1) + 4*n + 15; a(0) = 0. - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(19 - 15*x)/(1-x)^3.
E.g.f.: exp(x)*x*(19 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139581 a(n) = n(2n + 19).

Original entry on oeis.org

0, 21, 46, 75, 108, 145, 186, 231, 280, 333, 390, 451, 516, 585, 658, 735, 816, 901, 990, 1083, 1180, 1281, 1386, 1495, 1608, 1725, 1846, 1971, 2100, 2233, 2370, 2511, 2656, 2805, 2958, 3115, 3276, 3441, 3610, 3783, 3960, 4141

Offset: 0

Omar E. Pol, May 19 2008

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139579, A139580.

Table[n(2n+19),{n,0,50}]  (* Harvey P. Dale, Jan 26 2011 *)

a(n)=n*(2*n+19) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 19*n.
a(n) = a(n-1) + 4*n + 17 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(21 - 17*x)/(1-x)^3.
E.g.f.: exp(x)*x*(21 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A177731 Numbers which can be written as a sum of consecutive numbers, where the largest term in the sum is an odd number >= 3.

Original entry on oeis.org

5, 6, 9, 12, 13, 14, 15, 17, 18, 21, 22, 24, 25, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 53, 54, 55, 56, 57, 60, 61, 62, 63, 65, 66, 69, 70, 72, 73, 75, 76, 77, 78, 81, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 12 2010

nonn

Numbers of the form sum_{i=j..2k+1} i where j>=1 and 2k+1>j and k>=1. Numbers of the form (2k+1+j)*(2k+2-j)/2, j>=1, k>=1, 2k+1>j. - R. J. Mathar, Dec 04 2011
Subsequences include the A000384 where >=6, the A014106 where >=5, A071355 where >=12, A130861 where >=9, A139577 where >=13, A139579 where >=17 etc. The sequence is the union of all odd-indexed rows of A141419, except its first column and numbers <=3: {5,6}, {9,12,14,15}, {13,18,22,25,27,28}, ... - R. J. Mathar, Dec 04 2011
Does this sequence have asymptotic density 1? - Robert Israel, Nov 27 2018

			5=2+3, 6=1+2+3, 9=4+5, 12=3+4+5,...

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A177712, A136724, A177713.
Cf. A000384, A014106, A071355, A130861, A139577, A139579, A141419.
Contains A004766, A017137 and nonzero terms of A008588.
Disjoint from A002145.
Subsequence of A138591.

f:= proc(n) local r,k;
  for r in select(t -> (2*t-1)^2 >= 1+8*n, numtheory:-divisors(2*n) minus {2*n}) do
    k:= (r + 2*n/r - 3)/4;
    if k::posint and r >= 2*k+2 then return true fi
  od:
  false
end proc:
select(f, [$1..1000]); # Robert Israel, Nov 27 2018

z=200;lst1={};Do[c=a;Do[c+=b;If[c<=2*z,AppendTo[lst1,c]],{b,a-1,1,-1}],{a,1,z,2}];Union@lst1

cp's OEIS Frontend

A139576 a(n) = n*(2*n + 9).

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A139577 a(n) = n*(2*n + 11).

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A139578 a(n) = n*(2*n + 13).

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A139580 a(n) = n*(2*n + 17).

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A139581 a(n) = n*(2*n + 19).

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A177731 Numbers which can be written as a sum of consecutive numbers, where the largest term in the sum is an odd number >= 3.

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A139576 a(n) = n(2n + 9).

A139577 a(n) = n(2n + 11).

A139578 a(n) = n(2n + 13).

A139580 a(n) = n(2n + 17).

A139581 a(n) = n(2n + 19).