A000244 -id:A000244 - cp's OEIS frontend

A027472 Third convolution of the powers of 3 (A000244).

1, 9, 54, 270, 1215, 5103, 20412, 78732, 295245, 1082565, 3897234, 13817466, 48361131, 167403915, 573956280, 1951451352, 6586148313, 22082967873, 73609892910, 244074908070, 805447196631, 2646469360359, 8661172452084, 28242953648100, 91789599356325, 297398301914493, 960825283108362, 3095992578904722

Offset: 3

Olivier Gérard

Third column of A027465.

With offset = 2, a(n) is the number of length n words on alphabet {u,v,w,z} such that each word contains exactly 2 u's. - Zerinvary Lajos, Dec 29 2007

G. C. Greubel, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

Cf. A000244, A006043, A027465, A075513, A152818.

Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), this sequence (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), A027476 (q=15).

[3^(n-3)*Binomial(n-1, 2): n in [3..40]]; // G. C. Greubel, May 12 2021

nn=41; Drop[Range[0,nn]!CoefficientList[Series[Exp[x]^3 x^2/2!,{x,0,nn}],x],2] (* Geoffrey Critzer, Oct 03 2013 *)
LinearRecurrence[{9,-27,27}, {1,9,54}, 40] (* G. C. Greubel, May 12 2021 *)
Abs[Take[CoefficientList[Series[1/(1+3x^2)^3,{x,0,60}],x],{1,-1,2}]] (* Harvey P. Dale, Mar 03 2022 *)

a(n)=([0,1,0; 0,0,1; 27,-27,9]^(n-3)*[1;9;54])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

[3^(n-3)*binomial(n-1,2) for n in range(3, 40)] # Zerinvary Lajos, Mar 10 2009

Numerators of sequence a[3,n] in (b^2)[i,j]) where b[i,j] = binomial(i-1, j-1)/2^(i-1) if j <= i, 0 if j > i.
From Wolfdieter Lang: (Start)
a(n) = 3^(n-3)*binomial(n-1, 2).
G.f.: (x/(1-3*x))^3. (Third convolution of A000244, powers of 3.) (End)
a(n) = |A075513(n, 2)|/9, n >= 3.
a(n) = A152818(n-3,2)/2 = A006043(n-3)/2. - Paul Curtz, Jan 07 2009
The sequence 0, 1, 9, 54, ... has e.g.f.: (x + 3*x^2/2)*exp(3*x)/. - Paul Barry, Jul 23 2003
E.g.f.: E(0) where E(k) = 1 + 3*(2*k+3)*x/((2*k+1)^2 - 3*x*(k+2)*(2*k+1)^2/(3*x*(k+2) + 2*(k+1)^2/E(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 23 2012
With offset=2 e.g.f.: x^2*exp(3*x)/2. - Geoffrey Critzer, Oct 03 2013
From Amiram Eldar, Jan 05 2022: (Start)
Sum_{n>=3} 1/a(n) = 6 - 12*log(3/2).
Sum_{n>=3} (-1)^(n+1)/a(n) = 24*log(4/3) - 6. (End)

Corrected by T. D. Noe, Nov 07 2006
Better name from Wolfdieter Lang
Terms a(23) onward added by G. C. Greubel, May 12 2021

A036216 Expansion of 1/(1 - 3*x)^4; 4-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 12, 90, 540, 2835, 13608, 61236, 262440, 1082565, 4330260, 16888014, 64481508, 241805655, 892820880, 3252418920, 11708708112, 41712272649, 147219785820, 515269250370, 1789882659180, 6175095174171, 21171754882872

Offset: 0

Wolfdieter Lang

With three leading zeros, 3rd binomial transform of (0,0,0,1,0,0,0,0,...). - Paul Barry, Mar 07 2003

Number of n-permutations (n=4) of 4 objects u, v, w, z, with repetition allowed, containing exactly three u's. - Zerinvary Lajos, May 23 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Eric Weisstein's World of Mathematics, Idempotent Number.
Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), this sequence (m=3), A036217 (m=4), A036219 (m=5), A036220 (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

[3^n* Binomial(n+3, 3): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011

seq(3^n*binomial(n+3, 3), n=0..30)]; # Zerinvary Lajos, Dec 21 2006

CoefficientList[Series[1/(1-3x)^4,{x,0,30}],x] (* or *) LinearRecurrence[ {12,-54,108,-81},{1,12,90,540},30] (* Harvey P. Dale, Jul 27 2017 *)

a(n) = 3^n*binomial(n+3, 3) \\ Charles R Greathouse IV, Oct 03 2016

[3^n*binomial(n+3,3) for n in range(30)] # Zerinvary Lajos, Mar 10 2009

a(n) = 3^n*binomial(n+3, 3).
a(n) = A027465(n+4, 4).
G.f.: 1/(1 - 3*x)^4.
With three leading zeros, a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 81*a(n-4), a(0) = a(1) = a(2) = 0, a(3) = 1. - Paul Barry, Mar 07 2003
With three leading zeros, C(n, 3)*3^(n-3) is the second binomial transform of C(n, 3). - Paul Barry, Jul 24 2003
E.g.f.: (1/2)*(2 + 18*x + 27*x^2 + 9*x^3)*exp(3*x). - Franck Maminirina Ramaharo, Nov 23 2018
From Amiram Eldar, Jan 05 2022: (Start)
Sum_{n>=0} 1/a(n) = 36*log(3/2) - 27/2.
Sum_{n>=0} (-1)^n/a(n) = 144*log(4/3) - 81/2. (End)

A036217 Expansion of 1/(1-3*x)^5; 5-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 15, 135, 945, 5670, 30618, 153090, 721710, 3247695, 14073345, 59108049, 241805655, 967222620, 3794488740, 14635885140, 55616363532, 208561363245, 772903875555, 2833980877035, 10291825290285, 37050571045026

Offset: 0

Wolfdieter Lang

With a different offset, number of n-permutations (n=5) of 4 objects: u, v, z, x with repetition allowed, containing exactly four (4) u's. Example: a(1)=15 because we have uuuuv uuuvu uuvuu uvuuu vuuuu uuuuz uuuzu uuzuu uzuuu zuuuu uuuux uuuxu uuxuu uxuuu xuuuu. - Zerinvary Lajos, Jun 12 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (15,-90,270,-405,243).

Cf. A000332, A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), this sequence (m=4), A036219 (m=5), A036220 (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

[3^n* Binomial(n+4, 4): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011

seq(3^n*binomial(n+4,4), n=0..30); # Zerinvary Lajos, Jun 12 2008

CoefficientList[Series[1/(1-3x)^5,{x,0,30}],x] (* Harvey P. Dale, Jun 13 2017 *)

[3^n*binomial(n+4,4) for n in range(30)] # Zerinvary Lajos, Mar 10 2009

a(n) = 3^n*binomial(n+4, 4) = 3^n*A000332(n+4).
a(n) = A027465(n+5, 5).
G.f.: 1/(1-3*x)^5.
E.g.f.: (1/8)*(8 +96*x +216*x^2 +144*x^3 +27*x^4)*exp(3*x). - G. C. Greubel, May 19 2021
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 40 - 96*log(3/2).
Sum_{n>=0} (-1)^n/a(n) = 768*log(4/3) - 220. (End)

A036219 Expansion of 1/(1-3*x)^6; 6-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 18, 189, 1512, 10206, 61236, 336798, 1732104, 8444007, 39405366, 177324147, 773778096, 3288556908, 13660159464, 55616363532, 222465454128, 875957725629, 3400777052442, 13036312034361, 49400761393368, 185252855225130, 688082033693340, 2533392942234570

Offset: 0

Wolfdieter Lang

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729).

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), A036217 (m=4), this sequence (m=5), A036220 (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

[3^n*Binomial(n+5, 5): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

seq(3^n*binomial(n+5,5), n=0..30); # Zerinvary Lajos, Jun 13 2008

Table[3^n*Binomial[n+5, 5], {n, 0, 30}] (* G. C. Greubel, May 19 2021 *)
CoefficientList[Series[1/(1-3x)^6,{x,0,30}],x] (* or *) LinearRecurrence[ {18,-135,540,-1215,1458,-729},{1,18,189,1512,10206,61236},30] (* Harvey P. Dale, Jan 02 2022 *)

[3^n*binomial(n+5,5) for n in range(30)] # Zerinvary Lajos, Mar 10 2009

a(n) = 3^n*binomial(n+5, 5).
a(n) = A027465(n+6, 6).
G.f.: 1/(1-3*x)^6.
E.g.f.: (1/40)*(40 + 600*x + 1800*x^2 + 1800*x^3 + 675*x^4 + 81*x^5)*exp(3*x). - G. C. Greubel, May 19 2021
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 240*log(3/2) - 385/4.
Sum_{n>=0} (-1)^n/a(n) = 3840*log(4/3) - 4415/4. (End)

A036220 Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 21, 252, 2268, 17010, 112266, 673596, 3752892, 19702683, 98513415, 472864392, 2192371272, 9865670724, 43257171636, 185387878440, 778629089448, 3211844993973, 13036312034361, 52145248137444, 205836505805700, 802762372642230, 3096369151620030

Offset: 0

Wolfdieter Lang

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (21,-189,945,-2835,5103,-5103,2187).

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), A036217 (m=4), A036219 (m=5), this sequence (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

[3^n*Binomial(n+6, 6): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

seq(3^n*binomial(n+6,6), n=0..20); # Zerinvary Lajos, Jun 16 2008

Table[3^n*Binomial[n+6, 6], {n,0,30}] (* G. C. Greubel, May 19 2021 *)

[3^n*binomial(n+6,6) for n in range(30)] # Zerinvary Lajos, Mar 10 2009

a(n) = 3^n*binomial(n+6, 6).
a(n) = A027465(n+7,7).
G.f.: 1/(1-3*x)^7.
E.g.f.: (1/80)*(80 + 1440*x + 5400*x^2 + 7200*x^3 + 4050*x^4 + 972*x^5 + 81*x^6)*exp(3*x). - G. C. Greubel, May 19 2021
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 1173/5 - 576*log(3/2).
Sum_{n>=0} (-1)^n/a(n) = 18432*log(4/3) - 26508/5. (End)

A036221 Expansion of 1/(1-3*x)^8; 8-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 24, 324, 3240, 26730, 192456, 1250964, 7505784, 42220035, 225173520, 1148384952, 5637526128, 26778249108, 123591918960, 556163635320, 2447119995408, 10553204980197, 44695926974952, 186233029062300

Offset: 0

Wolfdieter Lang

With a different offset, number of n-permutations (n>=7) of 4 objects: u, v, z, x with repetition allowed, containing exactly seven (7) u's. Example: a(1)=24 because we have uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu. - Zerinvary Lajos, Jun 23 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (24,-252,1512,-5670,13608,-20412,17496,-6561).

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), A036217 (m=4), A036219 (m=5), A036220 (m=6), this sequence (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

[3^n*Binomial(n+7, 7): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

seq(3^n*binomial(n+7,7), n=0..30); # Zerinvary Lajos, Jun 23 2008

Table[3^n*Binomial[n+7,7], {n,0,30}] (* G. C. Greubel, May 19 2021 *)

[3^n*binomial(n+7, 7) for n in range(30)] # Zerinvary Lajos, Mar 13 2009

a(n) = 3^n*binomial(n+7, 7).
a(n) = A027465(n+8, 8.)
G.f.: 1/(1-3*x)^8.
E.g.f.: (1/560)*(560 +11760*x +52920*x^2 +88200*x^3 +66150*x^4 +23814*x^5 +3969*x^6 +243*x^7)*exp(3*x). - G. C. Greubel, May 19 2021
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 1344*log(3/2) - 5439/10.
Sum_{n>=0} (-1)^n/a(n) = 86016*log(4/3) - 247443/10. (End)

A036222 Expansion of 1/(1-3*x)^9; 9-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 27, 405, 4455, 40095, 312741, 2189187, 14073345, 84440070, 478493730, 2583866142, 13389124554, 66945622770, 324428787270, 1529449997130, 7035469986798, 31659614940591, 139674771796725, 605257344452475

Offset: 0

Wolfdieter Lang

With a different offset, number of n-permutations (n>=8) of 4 objects: u, v, z, x with repetition allowed, containing exactly eight (8) u's. Example: a(1)=27 because we have uuuuuuuuv, uuuuuuuuz, uuuuuuuux, uuuuuuuvu, uuuuuuuzu, uuuuuuuxu, uuuuuuvuu, uuuuuuzuu, uuuuuuxuu, uuuuuvuuu, uuuuuzuuu, uuuuuxuuu, uuuuvuuuu, uuuuzuuuu, uuuuxuuuu, uuuvuuuuu, uuuzuuuuu, uuuxuuuuu, uuvuuuuuu, uuzuuuuuu, uuxuuuuuu, uvuuuuuuu, uzuuuuuuu, uxuuuuuuu, vuuuuuuuu, zuuuuuuuu, xuuuuuuuu. - Zerinvary Lajos, Jun 23 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (27,-324,2268,-10206,30618,-61236,78732,-59049,19683).

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), A036217 (m=4), A036219 (m=5), A036220 (m=6), A036221 (m=7), this sequence (m=8), A036223 (m=9), A172362 (m=10).

[3^n*Binomial(n+8, 8): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

seq(3^n*binomial(n+8,8), n=0..18); # Zerinvary Lajos, Jun 23 2008

Table[3^n*Binomial[n+8, 8], {n, 0, 20}] (* Zerinvary Lajos, Jan 31 2010 *)
CoefficientList[Series[1/(1-3x)^9,{x,0,30}],x] (* or *) LinearRecurrence[{27,-324, 2268,-10206,30618,-61236,78732,-59049,19683}, {1,27,405,4455,40095,312741, 2189187,14073345,84440070}, 30] (* Harvey P. Dale, Jan 07 2016 *)

[3^n*binomial(n+8, 8) for n in range(30)] # Zerinvary Lajos, Mar 13 2009

a(n) = 3^n*binomial(n+8, 8).
a(n) = A027465(n+9, 9).
G.f.: 1/(1-3*x)^9.
a(0)=1, a(1)=27, a(2)=405, a(3)=4455, a(4)=40095, a(5)=312741, a(6)=2189187, a(7)=14073345, a(8)=84440070, a(n) = 27*a(n-1) - 324*a(n-2) + 2268*a(n-3) - 10206*a(n-4) + 30618*a(n-5) - 61236*a(n-6) + 78732*a(n-7) - 59049*a(n-8) + 19683*a(n-9). - Harvey P. Dale, Jan 07 2016
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 43632/35 - 3072*log(3/2).
Sum_{n>=0} (-1)^n/a(n) = 393216*log(4/3) - 3959208/35. (End)

A036223 Expansion of 1/(1-3*x)^10; 10-fold convolution of A000244 (powers of 3).

Original entry on oeis.org

1, 30, 495, 5940, 57915, 486486, 3648645, 25019280, 159497910, 956987460, 5454828522, 29753610120, 156206453130, 793048146660, 3908594437110, 18761253298128, 87943374834975, 403504896301650, 1815772033357425

Offset: 0

Wolfdieter Lang

With a different offset, number of n-permutations (n >= 9) of 4 objects: u, v, z, x with repetition allowed, containing exactly nine (9) u's. - Zerinvary Lajos, Jul 02 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (30,-405,3240,-17010,61236,-153090,262440,-295245,196830,-59049).

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), A036217 (m=4), A036219 (m=5), A036220 (m=6), A036221 (m=7), A036222 (m=8), this sequence (m=9), A172362 (m=10).

[3^n*Binomial(n+9, 9): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

seq(3^n*binomial(n+9, 9), n=0..20); # Zerinvary Lajos, Jul 02 2008

Table[3^n*Binomial[n+9,9], {n,0,30}] (* G. C. Greubel, May 18 2021 *)
CoefficientList[Series[1/(1-3x)^10,{x,0,30}],x] (* or *) LinearRecurrence[ {30,-405,3240,-17010,61236,-153090,262440,-295245,196830,-59049},{1,30,495,5940,57915,486486,3648645,25019280,159497910,956987460},30] (* Harvey P. Dale, Jan 16 2022 *)

[3^n*binomial(n+9,9) for n in range(30)] # Zerinvary Lajos, Mar 13 2009

a(n) = 3^n*binomial(n+9, 9).
a(n) = A027465(n+10, 10).
G.f.: 1/(1-3*x)^10.
E.g.f.: (4480 + 120960*x + 725760*x^2 + 1693440*x^3 + 1905120*x^4 + 1143072*x^5 + 381024*x^6 + 69984*x^7 + 6561*x^8 + 243*x^9)*exp(3*x)/4480. - G. C. Greubel, May 18 2021
From Amiram Eldar, Sep 22 2022: (Start)
Sum_{n>=0} 1/a(n) = 6912*log(3/2) - 784431/280.
Sum_{n>=0} (-1)^n/a(n) = 1769472*log(4/3) - 142532433/280. (End)

A074472 Length of iteration sequence of Collatz-function (A006370) when initial value is 3^n (A000244) and final cycle is followed once.

Original entry on oeis.org

1, 8, 20, 112, 23, 97, 34, 77, 76, 44, 136, 135, 134, 133, 145, 206, 130, 191, 141, 96, 95, 262, 429, 92, 259, 395, 332, 256, 255, 391, 390, 389, 463, 462, 461, 460, 459, 458, 457, 456, 455, 454, 502, 501, 451, 499, 498, 753, 496, 495, 494, 749, 492, 747, 490

Offset: 0

Labos Elemer, Sep 19 2002

nonn

			n=2: initial value=3^2, list of iterates is {9,28,14,7,22,11,34,17,52,26,13,50,20,10,5,16,8,4,2,1} length=a(2)=20; Observe that consecutive powers of 3 as arguments frequently provide iteration-lengths of consecutive integers, for instance n=10,11,12,13 give L=136,135,134,133 or n=88-96 result in L=1278-1271.

T. D. Noe, Table of n, a(n) for n = 0..1000

Cf. A000244, A006370, A008884, A075484-A075488.

f[x_] := (1-Mod[x, 2])*(x/2)+(Mod[x, 2])*(3*x+1); f[1]=1; Table[1+Length[FixedPointList[f, 3^w]], {w, 1, 100}]

A037095 "Sloping binary representation" of powers of 3 (A000244), slope = -1.

Original entry on oeis.org

1, 1, 3, 1, 3, 9, 11, 17, 19, 25, 123, 65, 195, 169, 171, 753, 435, 249, 2267, 4065, 8163, 841, 843, 31313, 29651, 39769, 38331, 30081, 160643, 49769, 53867, 563377, 700659, 1611961, 760731, 1207073, 5668771, 5566345, 11844619, 8699025, 10386067, 55868313

Offset: 0

Antti Karttunen, Jan 28 1999

			When powers of 3 are written in binary (see A004656), under each other as:
  000000000001 (1)
  000000000011 (3)
  000000001001 (9)
  000000011011 (27)
  000001010001 (81)
  000011110011 (243)
  001011011001 (729)
  100010001011 (2187)
and one collects their bits from the column-0 to NW-direction (from the least to the most significant end), one gets 1 (1), 01 (1), 011 (3), 0001 (1), 00011 (3), 001001 (9), etc. (See A105033 for similar transformation done on nonnegative integers, A001477).

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Cf. A105033, A000244, A037093, A037094, A037096, A037097, A339601.

A037095:= n-> add(bit_n(3^(n-i), i)*(2^i), i=0..n):
bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2):
seq(A037095(n), n=0..41);
# second Maple program:
b:= proc(n) option remember; `if`(n=0, 1, (p->
       expand((p-(p mod 2))*x/2)+3^n)(b(n-1)))
    end:
a:= n-> subs(x=2, b(n) mod 2):
seq(a(n), n=0..42);  # Alois P. Heinz, Dec 10 2020

A339601(n) = { my(m=1, s=0); while(n>=m, s += bitand(m,n); m <<= 1; n \= 3); (s); };
A037095(n) = A339601(3^n); \\ Antti Karttunen, Dec 09 2020

BINSLOPE(f) = n -> sum(i=0,n,bitand(2^(n-i),f(i))); \\ General transformation for these kinds of sequences.
A037095 = BINSLOPE(n -> 3^n); \\ And its application to A000244. - Antti Karttunen, Dec 09 2020

a(n) = A339601(A000244(n)). - Antti Karttunen, Dec 09 2020

Entry revised Dec 29 2007

More terms from Sean A. Irvine, Dec 08 2020

cp's OEIS Frontend

A027472 Third convolution of the powers of 3 (A000244).

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A036216 Expansion of 1/(1 - 3*x)^4; 4-fold convolution of A000244 (powers of 3).

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A036217 Expansion of 1/(1-3*x)^5; 5-fold convolution of A000244 (powers of 3).

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A036219 Expansion of 1/(1-3*x)^6; 6-fold convolution of A000244 (powers of 3).

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A036220 Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3).

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A036221 Expansion of 1/(1-3*x)^8; 8-fold convolution of A000244 (powers of 3).

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A036222 Expansion of 1/(1-3*x)^9; 9-fold convolution of A000244 (powers of 3).